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I work in PDEs. I have now written 3 papers. I find my style is of the form: introduction, statement of results, paragraphs to introduce something, lemma, more text, lemma, more text, lemma, more text, theorem, concluding remarks (I missed the proofs).

I am getting sick of this type of writing. I want to write my next paper with more style and elegance than something which looks like the output from a workhouse.

For example I have seen papers where they come up with some interesting result which they don't put into a lemma but instead put it in a paragraph. When I cite such a thing, I say something like "see the paragraph on page 10 of [1]" so I think it is a bad idea to put results outside environments.

Does anyone have any ideas? Basically I want to write a more unpredictable paper instead of the usual routine which I wish to take myself out of. This is good because readers will also find it more interesting.

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    $\begingroup$ An "interesting" paper is not necessarily a good paper. As you've just observed yourself, correct citation can become an issue when a paper gets too "interesting". And citability is one of the more important aspects of an academic paper. You write to make your results accessible and useable for other researchers. The usual definition-lemma-proof-lemma-proof-style is imho almost perfect for citing. In fact I've taken the habit of numbering each remark in between as well in case something's in it that's worth referencing/citing at a later point. $\endgroup$
    – Johannes Hahn
    Commented Jun 16, 2015 at 18:01
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    $\begingroup$ Meta discussion here: meta.mathoverflow.net/questions/2312/… For what it's worth, I think this site is the one best suited for this question, and that it's broadly on-topic as it pertains to the profession. However, I'm making it Community Wiki since there are likely to be a variety of opinions on the matter, and no definitive answer. (As I comment below, this post should probably not be migrated to MO meta.) $\endgroup$
    – Todd Trimble
    Commented Jun 16, 2015 at 18:38
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    $\begingroup$ I think that your penultimate paragraph contradicts the last one. As you say, we have structure for a reason; predictability is a virtue in formal scientific writing. The place of stylistic extravagance is taken by careful and rigorous writing; that is what a reader (at least I!) will appreciate. Save the rhetorical flourishes for expository writing, where they can be appreciated. $\endgroup$
    – LSpice
    Commented Jun 16, 2015 at 18:43
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    $\begingroup$ You may want to separate formal and informal discussion of the results into separate sections. So long as everything is clearly demarcated, both are useful to the reader. $\endgroup$
    – Lev Borisov
    Commented Jun 16, 2015 at 18:52
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    $\begingroup$ One thing that I like to do is have lemmas that can be described by a short phrase ("measurability of complementary spaces" etc). I think this helps the reader grasp the structure of the paper. Probably this is more utilitarian than artistic, but still... $\endgroup$
    – Anthony Quas
    Commented Jun 16, 2015 at 19:10

3 Answers 3

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Since the OP is looking for an alternative text structure, here's a possibility that I've seen in Dieudonné's multi-volume Eléments d'Analyse (Treatise on Analysis). He does not always put statements of lemmas or theorems, proofs and discussion in separate environments. Instead, breaks the text into numbered Chapters, Sections, and Subsections in the following way. Chapters and Sections have titles, while Subsections are anonymous and referred to only by number, like (23.3.10), with equations even further subnumbered, like (21.4.4.1). The point is that each Subsection is short enough to contain only one main idea, which could be a statement with or without proof, a remark, a definition, some motivational paragraphs, or an example. A definition or a statement could be highlighted in italics, but not in a separate environment.

It seems to me a decent compromise between citability and a more flexible text structure. As long as the Subsections are short enough, with the most important text somehow highlighted, the reader does not have to spend too much time looking for the information that is being referred to.

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  • $\begingroup$ Going from hazy memory, this is similar to the system used in Dixmier's books on von Neumann algebras and Cstar algebras $\endgroup$
    – Yemon Choi
    Commented Jun 16, 2015 at 21:14
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    $\begingroup$ I have grown used to this being the "French style". EGA is also written like this. (I like it a lot.) $\endgroup$
    – darij grinberg
    Commented Jun 16, 2015 at 22:13
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    $\begingroup$ The same works very well for Humphreys' "Reflection groups and Coxeter groups", but with only one-level-deep nesting. $\endgroup$
    – Chris Heunen
    Commented Jun 17, 2015 at 10:00
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    $\begingroup$ @darij grinberg, I wonder which is the first text written in the "French style". Is it "tractatus logico-philosophicus"? If so, "tree style" (as in "free style") seems a better naming. $\endgroup$
    – Uri Bader
    Commented Jul 19, 2021 at 22:23
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The mathematical papers I find most enjoyable (as well as accessible) are those written in order of increasing technicality. So, consider an order along the lines of Introduction and Conclusion (containing motivation, related work, main ideas, informal statement of results and applications, interesting open problems). Essential definitions. Formal statement of results. Applications/corollaries. Further definitions. Elementary arguments (may be several sections). Technical estimates (may be several sections). Of course, the logical dependences require careful cross-referencing.

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The only disadvantage of Dieudonne's style is that equation numbers are extremely long. I use this style with at most one point in subsections, theorem, lemmas (like 41.18), with local number insider subsections: (7), which I cite like that inside the subsection and cite like (41.18.7) from outside the subsection. All my books are written like that, and most papers. Unfortunately the Latex numbering does not support local numbers, so I use an extra program (called tex-nmb) for renumbering (written by Andreas Kriegl).

For a short paper I try to have one theorem in the beginning, one lemma, one corollary, one remark, without any numbers.

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